A YEAR ago, Laura Johnson was a high school dropout from New Mexico with green hair, multiple earrings, funky leather clothes, and a tattoo. She still is. But now she's also a straight-A student at City College of San Francisco, with a burning interest in science. For a nation increasingly concerned about its high school dropout rate - 28.9 percent and rising, according to US Education Secretary Lauro Cavazos - Miss Johnson has a story worth listening to.

Front and center in her story: the Exploratorium, a highly regarded, slightly offbeat museum of science (see box) that has a history of turning lives around.

``We came here, and we really, really liked it,'' says Johnson, recalling the first time she visited with her friend and fellow dropout, Liana Crouch. They spent some time talking to a few of the orange-jacketed teen-agers, who walk the floor and help visitors understand the exhibits - ``explainers,'' the museum calls them. Then they applied to join the Explainer Program.

Darlene Librero, coordinator of the Explainer Program, has no trouble with that idea. A former explainer herself, she knows what to look for: curiosity, enthusiasm, a willingness to mingle with people, and a sense that her staff is ``ticking inside - willing to try things out and move things around.'' In hiring explainers for the four- to five-month sessions (paying $4.25 an hour), she says, she pays no attention to the academic records. ``If we did that,'' she points out, ``we would probably lose some of the greatest explainers.''

Nor does a background in science matter. A study of the program, published in Science Education in 1987, found that only 54 percent of the more than 900 teen-agers hired as explainers since the museum opened in 1969 had an interest in science in high school. It also found that, despite studies showing that most working adolescents gain little of lasting benefit from their teen-age jobs, a brief stint as an explainer ``can substantially affect the teen-agers' later lives.''

The Explainer Program has been with the museum from the start. When physicist Frank Oppenheimer (who had worked with his brother, J. Robert Oppenheimer, building and testing the first atomic bomb at Los Alamos, N.M., in the 1940s) laid out his rationale for the Exploratorium in 1968, he recognized that many people think of science and technology ``as separate worlds that are harsh, fantastic, and hostile to humanity.'' The need, he recognized, was for exhibits ``designed to make things clearer rather than to cultivate obscurantism or science fiction.''

Central to the museum's goal is the demystification of science - a fact that explains the homemade appearance of the exhibits, which are built in a workshop, open to public view, behind a low fence. ``People who want polish and shine - there are lots of places they can go,'' says Caitlin Thomson, a museum aide and former explainer. Here, she notes proudly, ``not everything has a Formica top or is in a Plexiglas box.''

Johnson agrees. ``That's the whole idea - so that it doesn't appear so intimidating, so that it seems like everyday life,'' she says. ``Because that's what science is, it's everyday life.''

Pointing out the ``everyday'' qualities of science, rather than its great complexities, is the role of the explainers - a role that helps explain the choice of teen-agers. ``If we wanted [the explainers] to be science teachers, we would have hired science teachers,'' says Ms. Librero.

Although the Exploratorium provides about 50 hours of training to each new group of explainers, they are not expected to know all the answers. ``Explainers just walk around, and if you look like you're puzzled, they'll come over and talk to you about the exhibits,'' she adds. Their role, in fact, is less to explain than to help visitors ask the right questions.

And that, says museum publicist Linda Dackman, requires not only scientific understanding, but good personal relations. She sees the Exploratorium as ``a kind of humanistic place, where you learn the way that the world works without getting intimidated by the details.''

``There's an accessibility to everything that invites you to use it,'' says Jamie Bell, the assistant coordinator of the Explainer Program. He credits the simple, friendly construction of the exhibits with helping keep vandalism and theft to a minimum. The museum generally has little trouble with security, and the explainers provide the only security staff.

Ms. Crouch, now in her second semester as an explainer and, like Johnson, also enrolled in City College of San Francisco, notes that the job is ``as much learning as it is teaching.'' Recalling her high school science classes, she notes that ``I liked the microscopes, and that was about it.'' Otherwise, she found the teaching dry and distant - a factor contributing to her decision to drop out of school.

Interested in design, she was originally drawn to the Exploratorium because of an exhibit on computer art. Asked to assess the value of the explainer program in her own life, however, she points not to art or science, but to the humanistic qualities. ``I never enjoyed crowds,'' she says. Now, she says, she likes being with people and seeing them catch on to sometimes-difficult concepts.

Looking back on her own road from dropout to college student, Johnson points squarely to the role of the Exploratorium. ``I probably owe the reason that I want to do anything with myself now to this place,'' she says. ``When I was younger I was really interested in astronomy. But school just really bored me. I mean, science class was no fun, so I just dismissed it.

``Then I came here and realized that it actually is fun, and that I was right in the first place, and that science is a great thing. And now that I'm turned on to it, I can't get enough, I can't learn enough about it.''

Crouch agrees. ``If every science teacher I'd had in school had come to classes here,'' she says, ``I might not have quit school.''